Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer

TL;DR

This paper explores the effectiveness of a problem-inspired Variational Hamiltonian Ansatz in simulating 1D Hubbard chains on quantum computers, analyzing fidelity, physical properties, and noise mitigation strategies.

Contribution

It demonstrates the potential of the Variational Hamiltonian Ansatz to capture key physics of Hubbard chains and evaluates noise mitigation on real quantum hardware.

Findings

Low fidelity solutions accurately predict energy and double occupancy.

Spin-spin correlations are poorly captured even at high fidelity.

Noise mitigation strategies improve results on real quantum hardware.

Abstract

Hybrid quantum-classical algorithms have been proposed to circumvent noise limitations in quantum computers. Such algorithms delegate only a calculation of the expectation value to the quantum computer. Among them, the Variational Quantum Eigensolver (VQE) has been implemented to study molecules and condensed matter systems on small size quantum computers. Condensed matter systems described by the Hubbard model exhibit a rich phase diagram alongside exotic states of matter. In this manuscript, we try to answer the question: how much of the underlying physics of a 1D Hubbard chain is described by a problem-inspired Variational Hamiltonian Ansatz (VHA) in a broad range of parameter values ? We start by probing how much does the solution increases fidelity with increasing ansatz complexity. Our findings suggest that even low fidelity solutions capture energy and number of doubly occupied sites well, while spin-spin correlations are not well captured even when the solution is of high fidelity. Our powerful simulation platform allows us to incorporate a realistic noise model and shows a successful implementation of noise-mitigation strategies - post-selection and the Richardson extrapolation. Finally, we compare our results with an experimental realization of the algorithm on IBM Quantum's ibmq_quito device.